Britain's teachers deserve more sympathy. Any conversation about our economic and social ills almost always ends with the lowest common denominator agreement that education must be improved. Too many British children are not educated creatively to solve problems and are not in command of the basics. So runs the allegation and such failings are disguised by allegedly soft exams and grade inflation. Our teachers, by almost universal agreement, are letting the next generation down.

Yet there is one statistic that haunts me. A report last year found that five schools – St Paul's boys and girls, Westminster, Eton and Hills Road sixth form college in Cambridge (this last, unlike the others, in the state sector) – sent more students to Oxbridge over a period of three years than 2,000 other secondary schools combined. Around 35,000 children every year get the three As that could make them a candidate for our top universities; too few of them come from those 2,000 schools – the single biggest obstacle to promoting social mobility. Meanwhile, a third of this eligible pool of applicants come from private schools.

These are such alarming figures that much more is at work than any inadequacy on the part of our teachers. The army of teachers' critics too rarely acknowledges the many heartbreaking barriers to teaching well in so many of our schools – the children's disillusion and poverty, endemically disrupted classes and the recognition that however hard a pupil works he or she will never get a good job locally. The pupils and their schools are trapped.

But yet. To concede everything to broader economic and social forces is a counsel of despair. There are examples of brilliant schools in these areas; a well-led, dynamic school can become a site of hope and the unleashing of possibility. If the depressed parts of Britain are to break out of their spiral of decline, we have to start somewhere.

So it was good to hear Sir Michael Wilshaw, the incoming head of Ofsted, announcing in his first major speech last week that he would not tolerate the educational mediocrity that so besets Britain. Too many schools had been labelled as "outstanding" by Ofsted when they were not; he wanted outstanding to mean just that.

Wilshaw's aim is to create a "no-excuses" culture and he sees the indispensable means as stronger leadership in schools. Heads and their senior team should show their passion and commitment to teaching in everything they say or do, he said. They must be committed to professional development; they must ensure that performance management robustly rewards those who teach well. Equally, they must make sure something is done about those who consistently underperform.

Some individual heads rallied to his side, but then came the ritualistic condemnation from the teachers' unions. Chris Keates, general secretary of NASUWT, said Wilshaw "is trashing the school system, trashing the reputation of Ofsted… this is puerile game-playing at the expense of schools, their teachers and pupils". Even Malcolm Trobe, deputy general secretary of ASCL (which represents many heads), declared that Wilshaw's comments were "demoralising dedicated professionals… this is no way to improve our education system, nor to treat hard-working professionals".

So the battle lines are drawn. Keates and Trobe do speak for many teachers and heads who feel beleaguered and misunderstood. But defensive aggression in protection of the status quo, the default mode of so much contemporary trade unionism, will not advance the teachers' cause, the cause of education or the interests of their pupils. I know I dream, but imagine if the teachers' collective response had been to welcome Wilshaw's call to arms; to say that they agreed that it was a disgrace that thousands of our schools produced such woeful results; wanted to work wholeheartedly to improve leadership and agreed fully that good teachers should be acknowledged and rewarded; and action would be taken against poor performers. The nation would have applauded.

They could then have built on that bridgehead of support to argue that teachers could not fight this battle alone; that to inspire kids while doing so little to create possibilities for them once they leave school is betrayal; that to try and make any progress in the face of swingeing cuts in capital budgets and frozen teacher pay is to ask close to the impossible. They would do their part, but others should do theirs. In this way, teachers could transform themselves into the formidable leaders of a coalition pressing for broad-based economic and social improvement.

There will be teachers and heads who are desperate to open up such a national conversation, but their voices are drowned out. The heart of the problem is that teachers as a profession are reluctant to embrace the idea that there must be rewards and consequences for good and bad performance – the operational guts of what Wilshaw proposes when he argues for a no-excuses, performance-orientated culture in schools.

He has unexpected allies. The young Karl Marx criticised the utopian egalitarianism of the German socialists' Gotha programme by saying that socialists had to accept that good workers would expect the appropriate rewards, but would also expect the problem of shirkers and poor workers to be addressed.

Confronting poor performance is tough. It means establishing a framework so that teachers know what is expected, one that allows for tough conversations when those expectations are not met. It offers the chance of professional development but if that fails, teachers might lose not just pay but their jobs.

It also means that those who do well get quicker opportunities for promotion and salary hikes. To deliver such a regime demands incredible fortitude and determination from heads, along with the inspiration to show that it matters. Inevitably, they will be charged with being unfair and of victimising weaker colleagues. It is hard to marry performance with the collegiality of a staff room.

It is understandable why teacher unions are so resistant to performance-management: the doctrine is that teaching is a vocation and every teacher wants to do a good job. Performance-management is divisive. But yes, while everyone might want to do a good job, not everyone can or does. Not to manage performance is itself an extraordinary statement; it means giving up on trying to establish a framework for what good might look like and means selling the pass to state education's many enemies. Education, like the country, is at a crossroads. Having hundreds of underperforming schools is unacceptable. Wilshaw is right, and while his proposed changes won't alone do the job, they are a start. And they should be backed.